Multiple choice

The sum of all non-integer roots of the equation $x^{5} - 6x^{4} + 11x^{3} - 5x^{2} - 3x + 2 = 0$ is:

  1. $6$
  2. $-11$
  3. $-5$
  4. $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By checking for integer roots using the rational root theorem, we find x=1 and x=2 are roots. Dividing the polynomial by (x-1)(x-2) leaves a quadratic with non-integer roots. The sum of all roots is 6, and the sum of integer roots (1+2=3) leaves 3 as the sum of non-integer roots.

Keep practicing — related questions